import numpy as np
import pandas as pd
import matplotlib.pyplot as plt 
import networkx as nx
import folium
from IPython.display import HTML

df=pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/earthquakes-23k.csv')

t = Year
x = Latitude
y = Longitude
f = Magnitude

1. 데이터 정의

_df = df.assign(Year=list(map(lambda x: x.split('/')[-1], df.Date))).query('Year>="2000"').reset_index().iloc[:,1:]
_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 8744 entries, 0 to 8743
Data columns (total 5 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   Date       8744 non-null   object 
 1   Latitude   8744 non-null   float64
 2   Longitude  8744 non-null   float64
 3   Magnitude  8744 non-null   float64
 4   Year       8744 non-null   object 
dtypes: float64(3), object(2)
memory usage: 341.7+ KB

_df.Magnitude.hist()

<AxesSubplot:>

2. $f(x) = y$ 정의

$y$ = Magnitude, 지진 규모로 정의

f = _df.loc[:,"Magnitude"]

plt.plot(f,'-')

[<matplotlib.lines.Line2D at 0x7f8355974790>]

fig = plt.figure(figsize=(9, 6))
ax = fig.add_subplot(111, projection='3d')
img = ax.scatter(_df.Latitude, _df.Longitude, _df.Magnitude, c= _df.Magnitude,  cmap=plt.hot())
fig.colorbar(img)
plt.show()

lst=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,3]].\
to_numpy().tolist() for i in range(2016-2000)]

from folium import plugins 
data=(np.random.normal(size=(100,3)) + np.array([[28,77,5]])).tolist() # (좌표,weight)를 의미함, 그리고 numpy는 list가 될 수 없기 때문에 tolist 옵션 사용
m=folium.Map([28,77],zoom_start=6,scrollWheelZoom=False)
plugins.HeatMap(data).add_to(m)

<folium.plugins.heat_map.HeatMap at 0x7f835017e730>

m=folium.Map(scrollWheelZoom=False)
plugins.HeatMapWithTime(lst,radius=5,index=list(range(2000,2016))).add_to(m)
m

3. 비유클리드 공간에서의 거리 정의

$x$ = Latitude, 위도로 정의
$y$ = Longitude, 경도로 정의
지진의 영향이 주변에만 끼치는 것을 고려하여 경도, 위도의 차이가 90도 이내인 경우만 거리 계산

$$dist((x_i,y_i),(x_j,y_j)) = \sqrt{((x_j-x_i)^2+(y_j-y_i)^2}$$ $$\text{if } (x_j - x_i) \gt 90 \text{ and } \text{ } (y_j - y_i) \gt 90$$

def dist(i,j):
    if abs( _df.Latitude[j] - _df.Latitude[i] ) > 90: 
        return 10000  
    elif abs( _df.Longitude[j] - _df.Longitude[i] ) > 90: 
        return 10000
    else:
        return np.sqrt( ( ( _df.Latitude[j] - _df.Latitude[i] )**2) + ( ( _df.Longitude[j] - _df.Longitude[i])**2) )

4. 거리를 이용한 a weighted adjacency matrix $W_{i,j}$ 정의

$$W_{i,j}=\begin{cases}{exp(-\frac{[dist(i,j)]^2}{2\theta^2})} & \quad \text{if } dist(i,j) \leq κ \\ 0 & \quad \text{otherwise} \end{cases}$$

def weight(i,j,theta=150,kappa=1000):
    return np.exp( -np.abs(dist(i,j))**2 / (2*theta**2) ) if dist(i,j) <= kappa else 0

W = np.array([[weight(i,j) for i in range(len(_df))] for j in range(len(_df))])

plt.hist(W.reshape(-1))

(array([4.2284642e+07, 0.0000000e+00, 0.0000000e+00, 0.0000000e+00,
        0.0000000e+00, 0.0000000e+00, 2.1600000e+02, 5.4826600e+05,
        7.2334020e+06, 2.6391010e+07]),
 array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ]),
 <BarContainer object of 10 artists>)

그래프(임의보행 random walk)

nx.draw(nx.Graph(W))
# 저장하고 싶으면
# plt.show(
# plt.savefig("networkGraph.png")

5. $W_{i,j}$ 행렬을 이용한 차수 행렬 정의

$D$ = Degree Matrix

D = np.diag(W.sum(axis=1))

D

array([[3490.9134361 ,    0.        ,    0.        , ...,    0.        ,
           0.        ,    0.        ],
       [   0.        , 1783.14978455,    0.        , ...,    0.        ,
           0.        ,    0.        ],
       [   0.        ,    0.        , 1582.43548691, ...,    0.        ,
           0.        ,    0.        ],
       ...,
       [   0.        ,    0.        ,    0.        , ..., 4829.48599096,
           0.        ,    0.        ],
       [   0.        ,    0.        ,    0.        , ...,    0.        ,
        5070.23988759,    0.        ],
       [   0.        ,    0.        ,    0.        , ...,    0.        ,
           0.        , 4819.27276215]])

6. Graph Laplacian matrix 정의

$L = D - W$

L = D - W

L

array([[ 3.48991344e+03,  0.00000000e+00,  0.00000000e+00, ...,
         0.00000000e+00, -9.17030275e-01,  0.00000000e+00],
       [ 0.00000000e+00,  1.78214978e+03, -8.98356231e-01, ...,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00, -8.98356231e-01,  1.58143549e+03, ...,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       ...,
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,
         4.82848599e+03, -9.44181666e-01, -9.99973372e-01],
       [-9.17030275e-01,  0.00000000e+00,  0.00000000e+00, ...,
        -9.44181666e-01,  5.06923989e+03, -9.42335310e-01],
       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,
        -9.99973372e-01, -9.42335310e-01,  4.81827276e+03]])

7. 고유값 분해

${\bf L} = {\boldsymbol\Psi} {\boldsymbol\Lambda} {\boldsymbol\Psi}^\top$

λ, Ψ = np.linalg.eig(L)

Λ = np.diag(λ)

λ[0:20].round(3)

array([  -0.   ,   44.962,  698.037,  879.952,  891.986,  884.921,
        886.987,  983.406,  987.144,  991.654, 1000.049, 1035.996,
       1048.147, 1054.358, 1071.038, 1063.062, 1061.737, 1059.138,
       1058.526, 1058.733])

8. 주성분 분석

$compk = f @ np.outer(Ψ[:,k], Ψ[:,k]) $
- $k = 1, 2, 3, 8000$
$p = \sum_{1}^{n} comp1^2,\sum_{1}^{n} comp2^2,…,\sum_{1}^{n} compn^2$
$p = \frac{p}{\sum(p)}$

def comp(i):
    return (f @ np.outer( Ψ[:,i], Ψ[:,i]))

def p(i):
    return sum(comp(i)**2)

array_1 = np.array([p(i) for i in range(1,len(_df))])

varprop = array_1/array_1.sum()

_index = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop}).sort_values('varprop',ascending=False)
_indexlst = _index.iloc[:25,0].tolist()

_indexlst

[6152,
 3016,
 2178,
 5227,
 7571,
 5896,
 836,
 6818,
 6856,
 2337,
 6239,
 4957,
 3934,
 7573,
 3324,
 6618,
 6628,
 2494,
 857,
 6619,
 6813,
 1077,
 7292,
 4088,
 7948]

plt.plot( (f @ np.outer( Ψ[:,0], Ψ[:,0]))**2)
plt.ylim(0,40)

(0.0, 40.0)

fig,ax =plt.subplots(5,5)
k=0
for i in range(5):
    for j in range(5):
        ax[i][j].plot((f @ np.outer(Ψ[:,_indexlst[k]], Ψ[:,_indexlst[k]]))**2)
        # ax[i][j].set_ylim([-2,7])
        ax[i][j].set_title(k)
        k=k+1
fig.set_figwidth(16)            
fig.set_figheight(16)
fig.tight_layout()

9. PCA

comp1 = f @ np.outer( Ψ[:,0], Ψ[:,0])

comp2 = f @ np.outer( Ψ[:,_indexlst[0]], Ψ[:,_indexlst[0]])

comp3 = f @ np.outer( Ψ[:,_indexlst[1]], Ψ[:,_indexlst[1]])

comp4 = f @ np.outer( Ψ[:,_indexlst[2]], Ψ[:,_indexlst[2]])

comp5 = f @ np.outer( Ψ[:,_indexlst[3]], Ψ[:,_indexlst[3]])

comp6 = f @ np.outer( Ψ[:,_indexlst[4]], Ψ[:,_indexlst[4]])

_df["comp1"] = comp1

_df["comp2"] = comp2

_df["comp3"] = comp3

_df["comp4"] = comp4

_df["comp5"] = comp5

_df["comp6"] = comp6

_df["compall"] = comp1 + comp2 +comp3 + comp4 + comp5 + comp6

_df["compall2"] = comp2 +comp3 + comp4 + comp5 + comp6

_lst=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,3]].\
to_numpy().tolist() for i in range(2016-2000)]

__lst1=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,5]].\
to_numpy().tolist() for i in range(2016-2000)]

__lst2=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,6]].\
to_numpy().tolist() for i in range(2016-2000)]

__lst3=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,7]].\
to_numpy().tolist() for i in range(2016-2000)]

__lst4=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,8]].\
to_numpy().tolist() for i in range(2016-2000)]

__lst5=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,9]].\
to_numpy().tolist() for i in range(2016-2000)]

__lst6=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,10]].\
to_numpy().tolist() for i in range(2016-2000)]

__lstall=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,11]].\
to_numpy().tolist() for i in range(2016-2000)]

__lstall2=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,12]].\
to_numpy().tolist() for i in range(2016-2000)]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst2,radius=50,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

남태평양 (37.1557 144.6611, 37.3370 144.2370, 38.5060 141.9000, -7.7270 159.4750, 37.9300 143.8020, 37.9140 143.7640, 37.1057 144.6715, 37.9380 143.5990)
솔로몬해 (-9.3290 159.1673) 남서태평양 부근

_df.sort_values("comp2")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst3,radius=50,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

남대서양 (14.6682 -58.9272)
브라질 (-7.6060 -71.7220, -8.2950 -71.7380)
카리브 해 (10.9048 -62.3150, 11.1240 -62.5590) 브라질 위
볼리비아 (-19.2592 -63.9189)
콜롬비아 (4.3300 -73.7640)
콜롬비아 위쪽 부근 (7.0420 -77.8290)
베네수엘라 (10.4540 -63.4750)

_df.sort_values("comp3")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst4,radius=50,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

카롱가 말라위 (-10.126 33.870, -10.108 33.818)
남태평양 (56.594 -156.430, -36.129 -73.257, 58.235 -151.221, -36.217 -73.257)
칠레 (-36.074 -70.570)
미국 알레스카 코디악 섬 (57.369 -154.206, 57.401 -154.269)

_df.sort_values("comp4")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst5,radius=50,index=list(range(2000,2016))).add_to(_m)
_m

남태평양 (41.7150 144.0490, 42.3430 143.7640, 41.8070 144.2310, 41.8630 144.2090, 42.1590 144.0040)
코랄해 (-11.2397 161.8756, -11.1090 161.9150)
일본 (42.3950 142.9580, 42.4190 142.9130)

_df.sort_values("comp5")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst6,radius=50,index=list(range(2000,2016))).add_to(_m)
_m

인도네시아 (2.7070 96.0450, 2.6750 96.0620, -8.1935 117.8136, -4.0610 121.6940)
인도양 (3.5330 95.6580, -11.3750 115.0420)
말라카 (5.2834 96.1678) 알레스카, 미국
필리핀 (7.5930 124.0220)
셀레베스 해 (3.7330 124.6840) 인도네시아 필리핀 사이

_df.sort_values("comp6")[-10:-1]

Survey_Graph Signal Processing(fig1)

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lstall,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lstall2,radius=50,index=list(range(2000,2016))).add_to(_m)
_m

_G = nx.Graph(W-np.identity(len(f)))

_pos = nx.spring_layout(_G,iterations=20)

m_pos = list(zip(_df.Latitude,_df.Longitude))

fig,ax = plt.subplots(figsize = (16,8))
plt.title('on Map')
nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=λ,node_size = 50, ax=ax)
edges = nx.draw_networkx_edges(_G,m_pos,edge_color='k' ,width=0.1, edge_cmap=plt.cm.Blues,ax=ax)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
plt.title('on Map')
nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.Magnitude[:300],node_size = 50, ax=ax)
edges = nx.draw_networkx_edges(_G,m_pos,edge_color='k' ,width=0.1, edge_cmap=plt.cm.Blues,ax=ax)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
plt.title('on Map')
nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp1[:300],node_size = 50, ax=ax)
edges = nx.draw_networkx_edges(_G,m_pos,edge_color='k' ,width=0.1, edge_cmap=plt.cm.Blues,ax=ax)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
plt.title('on Map')
nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp2[:300],node_size = 50, ax=ax)
edges = nx.draw_networkx_edges(_G,m_pos,edge_color='k' ,width=0.1, edge_cmap=plt.cm.Blues,ax=ax)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
plt.title('on Map')
nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp3[:300],node_size = 50, ax=ax)
edges = nx.draw_networkx_edges(_G,m_pos,edge_color='k' ,width=0.1, edge_cmap=plt.cm.Blues,ax=ax)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
plt.title('on Map')
nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.compall[:300],node_size = 50, ax=ax)
edges = nx.draw_networkx_edges(_G,m_pos,edge_color='k' ,width=0.1, edge_cmap=plt.cm.Blues,ax=ax)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
plt.title('on Map')
nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.compall2[:300],node_size = 50, ax=ax)
edges = nx.draw_networkx_edges(_G,m_pos,edge_color='k' ,width=0.1, edge_cmap=plt.cm.Blues,ax=ax)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5	comp6
5202	01/17/2010	37.9380	143.5990	5.6	2010	5.877395	0.080330	0.000017	-0.000039	-0.000390	0.000062
7269	10/25/2013	37.1057	144.6715	5.5	2013	5.877395	0.081572	0.000017	-0.000039	-0.000364	0.000068
6863	12/07/2012	37.9140	143.7640	6.2	2012	5.877395	0.091564	0.000017	-0.000039	-0.000392	0.000063
5847	03/11/2011	37.9300	143.8020	6.3	2011	5.877395	0.107747	0.000017	-0.000039	-0.000392	0.000063
8589	09/14/2016	-9.3290	159.1673	6.0	2016	5.877395	0.119531	0.000019	-0.000038	-0.000063	0.000086
2540	01/22/2005	-7.7270	159.4750	6.4	2005	5.877395	0.120563	0.000019	-0.000038	-0.000025	0.000091
3018	12/16/2005	38.5060	141.9000	6.0	2005	5.877395	0.123177	0.000017	-0.000039	-0.000428	0.000049
5863	03/11/2011	37.3370	144.2370	6.1	2011	5.877395	0.143002	0.000017	-0.000039	-0.000384	0.000065
7267	10/25/2013	37.1557	144.6611	7.1	2013	5.877395	0.685526	0.000017	-0.000039	-0.000378	0.000068

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5	comp6
5200	01/15/2010	10.4540	-63.4750	5.6	2010	5.877395	-0.000006	0.068093	-0.004054	-9.902094e-07	9.178107e-06
431	11/08/2000	7.0420	-77.8290	6.5	2000	5.877395	-0.000003	0.086172	-0.001590	-4.565092e-07	-1.454736e-06
4346	05/24/2008	4.3300	-73.7640	5.9	2008	5.877395	-0.000004	0.091330	-0.001757	-5.569279e-07	2.799644e-07
7370	01/27/2014	-19.2592	-63.9189	5.6	2014	5.877395	-0.000005	0.126530	-0.003673	-8.966770e-07	8.048556e-06
371	10/04/2000	11.1240	-62.5590	6.2	2000	5.877395	-0.000006	0.130404	-0.003128	-1.046387e-06	1.054049e-05
1342	10/12/2002	-8.2950	-71.7380	6.9	2002	5.877395	-0.000004	0.166766	-0.001707	-5.638365e-07	3.726622e-07
7251	10/12/2013	10.9048	-62.3150	6.0	2013	5.877395	-0.000006	0.210905	-0.002979	-1.051451e-06	1.068778e-05
1639	06/20/2003	-7.6060	-71.7220	7.1	2003	5.877395	-0.000004	0.266692	-0.001724	-5.638442e-07	3.748997e-07
7393	02/18/2014	14.6682	-58.9272	6.5	2014	5.877395	-0.000006	0.948964	-0.003036	-1.228123e-06	1.586936e-05

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5	comp6
245	07/11/2000	57.401	-154.269	5.5	2000	5.877395	8.287029e-07	0.002763	0.063033	1.075998e-07	2.027612e-07
5345	03/16/2010	-36.217	-73.257	6.7	2010	5.877395	-3.243943e-06	-0.000569	0.063623	-4.518802e-07	1.700581e-07
1957	01/20/2004	58.235	-151.221	5.5	2004	5.877395	8.796409e-07	0.002008	0.067790	1.172173e-07	1.138469e-07
5152	12/19/2009	-10.108	33.818	6.0	2009	5.877395	6.098090e-05	0.002925	0.081454	2.222834e-05	-7.870314e-04
244	07/11/2000	57.369	-154.206	6.6	2000	5.877395	8.322470e-07	0.003037	0.086612	1.081114e-07	2.014678e-07
6646	06/07/2012	-36.074	-70.570	6.0	2012	5.877395	-3.280917e-06	-0.000873	0.098309	-4.720510e-07	5.258293e-07
5286	02/27/2010	-36.129	-73.257	5.5	2010	5.877395	-3.245256e-06	-0.000531	0.141829	-4.520672e-07	1.703117e-07
7993	05/29/2015	56.594	-156.430	6.7	2015	5.877395	8.117625e-07	0.001272	0.215134	1.043589e-07	2.337824e-07
5132	12/06/2009	-10.126	33.870	5.8	2009	5.877395	6.088868e-05	0.002950	0.296198	2.224737e-05	-7.809752e-04

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5	comp6
3655	03/18/2007	42.1590	144.0040	5.5	2007	5.877395	-0.002861	0.000017	-0.000039	0.015418	0.000058
2046	03/26/2004	41.8630	144.2090	5.8	2004	5.877395	-0.002826	0.000018	-0.000039	0.015873	0.000059
1782	09/25/2003	41.8070	144.2310	5.5	2003	5.877395	-0.002838	0.000018	-0.000039	0.017358	0.000059
1779	09/25/2003	42.3430	143.7640	5.5	2003	5.877395	-0.002912	0.000017	-0.000039	0.018660	0.000056
2349	11/11/2004	-11.1090	161.9150	5.5	2004	5.877395	-0.003910	0.000020	-0.000037	0.031188	0.000083
6734	08/25/2012	42.4190	142.9130	5.9	2012	5.877395	-0.003042	0.000017	-0.000039	0.067206	0.000051
2149	06/10/2004	42.3950	142.9580	5.8	2004	5.877395	-0.003045	0.000017	-0.000039	0.074431	0.000051
7493	04/14/2014	-11.2397	161.8756	5.8	2014	5.877395	-0.003892	0.000020	-0.000037	0.089764	0.000083
2361	11/14/2004	41.7150	144.0490	5.5	2004	5.877395	-0.002968	0.000017	-0.000039	0.191433	0.000058

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5	comp6
3509	12/12/2006	3.7330	124.6840	6.3	2006	5.877395	0.000300	-9.462553e-06	-0.000041	-0.000053	0.173008
6206	07/11/2011	-4.0610	121.6940	5.5	2011	5.877395	0.000246	6.047089e-07	0.000014	-0.000071	0.213636
1190	06/14/2002	7.5930	124.0220	5.6	2002	5.877395	0.000333	-8.566473e-06	-0.000043	-0.000043	0.224372
8529	07/31/2016	-8.1935	117.8136	5.6	2016	5.877395	0.000241	-6.365248e-06	0.000019	-0.000076	0.279446
8698	12/06/2016	5.2834	96.1678	6.5	2016	5.877395	0.000409	3.648001e-06	0.000043	-0.000041	0.287317
5151	12/19/2009	2.6750	96.0620	5.5	2009	5.877395	0.000389	3.583999e-06	0.000043	-0.000047	0.298019
887	09/20/2001	-11.3750	115.0420	5.6	2001	5.877395	0.000236	-1.214039e-05	0.000023	-0.000081	0.338343
1033	01/24/2002	3.5330	95.6580	5.7	2002	5.877395	0.000397	3.140678e-06	0.000043	-0.000045	0.432146
6698	07/25/2012	2.7070	96.0450	6.4	2012	5.877395	0.000390	3.582331e-06	0.000043	-0.000047	1.123773